SMARANDACHE-BOOLEAN-NEAR-RINGS AND BOOLEAN-Ⅰ-ALGEBRA

摘要

In this paper we introduced Smarandache-2-algebraic structure of Boolean-near-ring namely Smarandache-Boolean-near-ring. A Smarandache-2-algebraic structure on a set N means a weak algebraic structure A_0 on N such that there exist a proper subset M of N, which is embedded with a stronger algebraic structure A_1, stronger algebraic structure means satisfying more axioms, by proper subset one understands a subset different from the empty set, from the unit element if any, from the whole set. We define Smarandache-Boolean-near-ring and obtain some of its characterization through Boolean-ring and Lattice Ordered groups Ⅱ. For basic concept of near-ring we refer to G. Pliz.